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Research Objective

To propose and evaluate a new unit interval probability distribution, the Unit Nadarajah-Haghighi (UNH) distribution, for modeling unit interval data, specifically focusing on the recovery rate of COVID-19 and milk production data.

Methodology

The study proposes the Unit Nadarajah-Haghighi (UNH) distribution by transforming the Nadarajah-Haghighi distribution (NHD) to fit data within the unit interval (0, 1). The methodology involves deriving the probability density function (pdf), cumulative distribution function (cdf), and various statistical properties including reliability measures (survival function, hazard rate function, cumulative hazard rate function, reversed hazard rate function), moments, quantile function, and entropy measures (Rényi, Tsallis, Arimoto). Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method, with parameter values estimated using the Newton-Raphson method in R. A simulation study is conducted to assess the behavior of the estimated parameters. The UNH distribution is then applied to two real-world datasets: COVID-19 recovery rates in Turkey and milk production data, with performance evaluated using goodness-of-fit tests like the Kolmogorov-Smirnov (KS) and Cramer-von Mises (CVM) tests.

Methodology Flowchart

                        graph TD
    A["Define Nadarajah-Haghighi Distribution NHD"] --> B["Transform NHD to Unit Interval UNH Distribution"];
    B --> C["Derive UNH PDF and CDF"];
    C --> D["Study Statistical Properties Reliability, Moments, Entropy, Order Statistics"];
    D --> E["Estimate Parameters using MLE"];
    E --> F["Conduct Simulation Study"];
    F --> G["Apply UNH to Real Data COVID-19 Recovery, Milk Production"];
    G --> H["Evaluate Goodness-of-Fit KS, CVM Tests"];
    H --> I["Compare UNH with Other Distributions"];
    I --> J["Draw Conclusions and Discuss Implications"];                    

Discussion

The UNH distribution is presented as a valuable addition to the family of unit interval distributions, offering advantages such as a flexible density and hazard rate function, which are crucial for modeling diverse datasets. The study highlights the importance of developing new statistical models to accurately capture the complexities of phenomena like disease recovery rates and production data. The UNH distribution's ability to provide a good fit to real-world data, as demonstrated by the goodness-of-fit tests, supports its utility. The paper also emphasizes the role of statisticians and policymakers in using such models for prediction and prevention of future epidemics.

Key Findings

The proposed UNH distribution exhibits flexibility with various shapes for its pdf and hazard rate function, making it suitable for different types of unit interval data. Simulation studies indicate that Mean Squared Error (MSE) and bias decrease as sample size increases. Application to COVID-19 recovery rates in Turkey showed that UNH achieved the minimum KS test statistic and maximum p-value, indicating a good fit. For milk production data, UNH also demonstrated competitive performance. The entropy values for UNH are observed to be lower, suggesting less uncertainty.

Conclusion

The Unit Nadarajah-Haghighi (UNH) distribution is a novel and flexible model for unit interval data. Its application to COVID-19 recovery rates and milk production data demonstrates its effectiveness and competitiveness compared to existing distributions. The UNH distribution's ability to model diverse data shapes and its favorable statistical properties make it a useful tool for analysis and prediction in various fields, including public health and agriculture.

Fact Check

1. COVID-19 First Recovery Case in Turkey: The text states the World Health Organization (WHO) reported the first recovery case in Turkey on March 26, 2020.
2. Number of COVID-19 Recovery Rate Observations: The text mentions 25 observations on daily recovery rates in Turkey between March 27 and April 20.
3. Number of Milk Production Data Observations: The text states the milk production data is from 107 SNDI race cows.

Mind Map